Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?

Dotty Six is a simple dice game that you can adapt in many ways.

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

There were 22 legs creeping across the web. How many flies? How many spiders?

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

Can you score 100 by throwing rings on this board? Is there more than way to do it?

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Here is a chance to play a version of the classic Countdown Game.

There are nasty versions of this dice game but we'll start with the nice ones...

Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Use the number weights to find different ways of balancing the equaliser.

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Can you hang weights in the right place to make the equaliser balance?

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

How would you count the number of fingers in these pictures?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.

An environment which simulates working with Cuisenaire rods.

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

On Planet Plex, there are only 6 hours in the day. Can you answer these questions about how Arog the Alien spends his day?